scholarly journals The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds

2016 ◽  
Vol 55 (6) ◽  
Author(s):  
Huagui Duan ◽  
Yiming Long ◽  
Wei Wang
Keyword(s):  
Closed Geodesics ◽  
Finsler Manifolds ◽  
Common Index

scholarly journals Multiple Closed Geodesics on Positively Curved Finsler Manifolds

2019 ◽  
Vol 19 (3) ◽  
pp. 495-518 ◽  
Author(s):  
Wei Wang
Keyword(s):  
Finsler Manifold ◽  
Flag Curvature ◽  
Closed Geodesics ◽  
Finsler Manifolds ◽  
Positively Curved

Abstract In this paper, we prove that on every Finsler manifold {(M,F)} with reversibility λ and flag curvature K satisfying {(\frac{\lambda}{\lambda+1})^{2}<K\leq 1} , there exist {[\frac{\dim M+1}{2}]} closed geodesics. If the number of closed geodesics is finite, then there exist {[\frac{\dim M}{2}]} non-hyperbolic closed geodesics. Moreover, there are three closed geodesics on {(M,F)} satisfying the above pinching condition when {\dim M=3} .

scholarly journals A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Muhammad Hamid ◽  
Wei Wang
Keyword(s):  
Closed Geodesic ◽  
Poincaré Map ◽  
Finsler Manifold ◽  
Flag Curvature ◽  
Poincare Map ◽  
Closed Geodesics ◽  
Symmetric Property ◽  
Geodesic Problem ◽  
Common Index

<p style='text-indent:20px;'>In this paper, we prove a symmetric property for the indices for symplectic paths in the enhanced common index jump theorem (cf. Theorem 3.5 in [<xref ref-type="bibr" rid="b6">6</xref>]). As an application of this property, we prove that on every compact Finsler manifold <inline-formula><tex-math id="M1">\begin{document}$ (M, \, F) $\end{document}</tex-math></inline-formula> with reversibility <inline-formula><tex-math id="M2">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula> and flag curvature <inline-formula><tex-math id="M3">\begin{document}$ K $\end{document}</tex-math></inline-formula> satisfying <inline-formula><tex-math id="M4">\begin{document}$ \left(\frac{\lambda}{\lambda+1}\right)^2&lt;K\le 1 $\end{document}</tex-math></inline-formula>, there exist two elliptic closed geodesics whose linearized Poincaré map has an eigenvalue of the form <inline-formula><tex-math id="M5">\begin{document}$ e^{\sqrt {-1}\theta} $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M6">\begin{document}$ \frac{\theta}{\pi}\notin{\bf Q} $\end{document}</tex-math></inline-formula> provided the number of closed geodesics on <inline-formula><tex-math id="M7">\begin{document}$ M $\end{document}</tex-math></inline-formula> is finite.</p>

scholarly journals Two closed geodesics on compact simply connected bumpy Finsler manifolds

2016 ◽  
Vol 104 (2) ◽  
pp. 275-289 ◽  
Author(s):  
Huagui Duan ◽  
Yiming Long ◽  
Wei Wang
Keyword(s):  
Closed Geodesics ◽  
Finsler Manifolds ◽  
Simply Connected

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

scholarly journals Sufficient Criteria for Obtaining Hardy Inequalities on Finsler Manifolds

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
Ágnes Mester ◽  
Ioan Radu Peter ◽  
Csaba Varga
Keyword(s):  
Finsler Manifolds ◽  
Hardy Inequalities

scholarly journals Angular self-intersections for closed geodesics on surfaces

2005 ◽  
Vol 134 (02) ◽  
pp. 419-426 ◽  
Author(s):  
Mark Pollicott ◽  
Richard Sharp
Keyword(s):  
Closed Geodesics
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